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Chapter 9: Q7. (page 336)

a.What do you think is true of common external tangents AB炉and CD炉?prove it.

b.Will your results in part abe true if the circles are congruent?

Short Answer

Expert verified

(a)

The tangent AB is congruent to tangent CD.

Step by step solution

01

Step 1. Given information.

The figure here given is,

02

Step 2. Concept used.

In the given figure, BZ and DZ are tangents.

If circle has a two tangent from a unique point then there are equal,

BZ=DZ and AZ=CZ........1

The sum of BA and AZ is DZ

03

Step 3. This implies as shown below.

BZ=DZBA+AZ=DC+CZ

It is known that AZ=CZfrom (1)

Subtract AZ from both sides to get,

BA=DC

Therefore, it is proved that AB鈮�CD.

b

Yes, the results in part a holds good if the circles are congruent.

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